Question: $T(t)$ models the daily high temperature (in $^\circ C$ ) in Santiago, Chile, $t$ days after the hottest day of the year. Here, $t$ is entered in radians. $T(t) = 7.5\cos\left(\dfrac{2\pi}{365}t\right) + 21.5$ What is the second time after the hottest day of the year that the daily high temperature is $20^\circ C$ ? Round your final answer to the nearest whole day.
Answer: Converting the problem into mathematical terms $T(t) = 7.5\cos\left({\dfrac{2\pi}{365}}t\right) + 21.5$ has a period of $\dfrac{2\pi}{{\scriptsize\dfrac{2\pi}{365}}}=365$ days. We want to find the second solution to the equation $T(t)=20$ within the period $0<t<365$. The answer The equation's two solutions within the desired period (rounded to the nearest whole day) are $103$ and $262$. Therefore, the second time that the daily high temperature hits $20^\circ C$ is after $262$ days after the hottest day of the year.